kmill

16 ms·

121.
by kmill 5y ago
I don't know too much about it, other than that a symplectic geometer friend helped out, but light field networks seem interesting: https://www.vincentsitzmann.com/lfns/ Something I've thought would be intere
122.
by kmill 5y ago
There is nothing at all preventing the existence of multiple distributive laws, and I can think of some (non-programmy) examples that have multiple possibilities. I wouldn't be surprised if some cohomology group classifies them, at lea
123.
by kmill 5y ago
I can't say I fully understand it, but having compared major triads with different intonations, I can only say I myself find slightly sharper thirds to sound nicer in chords. Here's one thing I've used: http://tmp
124.
by kmill 5y ago
I brought up string quartets because I know about tuning them, and, like barbershop quartets, it's 4-part harmony with extremely harmonic instruments. Bowing a string causes a phenomenon called "mode locking," where the norm
125.
by kmill 5y ago
I think one of the reasons ii V I is so compelling (versus IV V I) is that the ii (or ii7) is conflating many notes. In C major, using interval terms as a stand-in for "tuned justly": Is the D a fourth below G or a minor (or harm
126.
by kmill 5y ago
That's a nice thought in theory, but I can assure you that string quartets do not play 5:4 major thirds -- they're significantly sharper (but not quite equal tempered major thirds). There's more to music than acoustics. Four-
127.
by kmill 5y ago
You might like the book "Equal Temperament Ruined Harmony." It makes the case that there is a long history of differentiating sharps and flats in western music (flats are just a bit sharper than sharps), while arguing that in prac
128.
by kmill 5y ago
It's not very precise talking about whether a monad commutes -- it's not clear what "commutes" should really mean (certainly not F . G = G . F since that's way too restrictive). I started working it out by hand, but
129.
by kmill 5y ago
Here's my one weird trick: work toward a PhD in mathematics, then get a postdoc, where you finally get assigned to teach courses like upper division undergraduate number theory. Thanks to this experience, I can tell you immediately wha
130.
by kmill 5y ago
The article is taking the first-order approximation of the doubling equation for discrete compounding interest, and as it turns out this value does not change no matter the compounding frequency. For different compounding frequencies, the v
131.
by kmill 5y ago
What a strange coincidence: 17 hours ago Edward Kmett tweeted about Dunning-Kruger https://twitter.com/kmett/status/1485464550786883588?s=20
132.
by kmill 5y ago
Yeah, it's sort of like saying "the knife didn't cause them to die, they were just an undiagonosed hemophiliac and the wound failed to close properly." However, teasing out the steelman from this, what they mean is &quot
133.
by kmill 5y ago
What about ker, coker, im, hom, end, aut, lim, colim, Set, Top, Man, Mat, Vect, GL, SL, SO, Lie, Gr, Tor, Ext, tr, Rep, char, rank, Isom, ann, hull, Diff, ...? I'm just copying multiletter names out of my preamble.tex file here. I get
134.
by kmill 5y ago
Speaking of which, there's a comment today about SICM in Clojure: https://news.ycombinator.com/item?id=29714267
135.
by kmill 5y ago
You might like Structure and Interpretation of Classical Mechanics by Sussman and Wisdom. It does classical mechanics using an MIT-Scheme library. Lean/mathlib is a mix of functional programming and classical math notation. The communi
136.
by kmill 5y ago
> Is all perceived complexity in math inherent to it No, of course not, but I'd argue that every notation that's in use gives practitioners that use it strictly more mathematical capability. Notations make things that previousl
137.
by kmill 5y ago
It's fine, you just add a space. It's also used for function application, like "sin x". I'd say single-letter variable names are mostly due to ease of handwriting when doing calculations (or for giving a chalkboard
138.
by kmill 5y ago
> preventing students to think of math as lego bricks in which you can use a set of functions to build newer functions Isn't this something that mathematical notation lets you be able to see at all? (I'm also not sure what you
139.
by kmill 5y ago
As Wikipedia has on the page on Euler diagrams: https://commons.wikimedia.org/wiki/File:Euler_and_Venn_diagr...
140.
by kmill 5y ago
That page is incorrect about GHC's memory management -- I verified this with a question to haskell-cafe around 2014, and I guess no one got around to updating it. The linked paper at the bottom of the article explains how things work a
141.
by kmill 5y ago
In this case it's a description of the 6-dimensional coordinates used in Lagrangian mechanics, which dates to the late 1700s. https://en.wikipedia.org/wiki/Lagrangian_mechanics https://en.wikipedia.org&
142.
by kmill 5y ago
Direct links to the papers: https://www.nature.com/articles/s41586-021-04086-x "Advancing mathematics by guiding human intuition with AI" https://arxiv.org/abs/2111.15323 "The signa
143.
by kmill 5y ago
Here's a take from a mathematician-in-training, and it's biased toward research-level math, or at least math from the last hundred years: Math is difficult, and a lot of what we have is the result of the sharpest minds doing their
144.
by kmill 5y ago
The idea is that if you have a bipartite graph and the sets V and W are the vertex sets for the bipartition, then V is the hypergraph's vertices and W is the hypergraph's hyperedges. A hyperedge w in W is incident to whatever it&
145.
by kmill 5y ago
What's the argument here? That it's difficult to learn to use a subset of a language because it is frustrating to locate the boundaries? Isn't it more frustrating to learn a completely unknown language? Maybe what you're
146.
by kmill 5y ago
I think an approximation to this in C++ would be to have some thread-local objects called condition handlers that you set using some RAII construct (so, something that will replace the current condition handler and then later restore it whe
147.
by kmill 5y ago
> No, I'm not conflating them. Earlier you said "¼ and 1/4 are the same symbol" but now you're saying that symbols are physical things that unambiguously map onto a single equivalence class called a "conce
148.
by kmill 5y ago
This is either quite the claim or you have a non-standard definition of "symbol." Each of those three representations are obviously different, though they all refer to the concept of "one-quarter," and I very much quest
149.
by kmill 5y ago
I see, so as a low-dimensional topologist I'm not a mathematician, thanks!* But more seriously, if you haven't read it already you might take a look at Thurston's "On Proof and Progress in Mathematics." He had a st
150.
by kmill 5y ago
Ah, I see you're a mathematical formalist. That's one philosophy of what math is, but it's not the only one. What's going on in my mind when I visualize 3-dimensional manifolds and manipulate them? Cutting pieces apart,

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